A119833 Primes p such that 2*p#-1 is prime.

2, 3, 5, 7, 17, 19, 37, 71, 79, 113, 857, 863, 16361, 62989

Offset

1,1

Links

Table of n, a(n) for n=1..14.

Example

2*2 - 1 = 3, 3 prime so a(1)=2;
2*2*3 - 1 = 11, 11 prime so a(2)=3;
2*2*3*5 - 1 = 59, 59 prime so a(3)=5.

Mathematica

Module[{nn=900, pr, pl}, pr=Prime[Range[nn]]; pl=FoldList[Times, pr]; Select[ Thread[{pr, pl}], PrimeQ[2*#[[2]]-1]&][[All, 1]]] (* Harvey P. Dale, May 02 2018 *)

Prog

(Magma) [p:p in PrimesUpTo(4000)|IsPrime(2*&*PrimesUpTo(p)-1)]; // Marius A. Burtea, Mar 25 2019
(Python)
from sympy import isprime, nextprime
def afind(limit):
    p = 2
    twoprimorialp = 4
    while p <= limit:
        if isprime(twoprimorialp - 1):
            print(p, end=", ")
        p = nextprime(p)
        twoprimorialp *= p
afind(1000) # Michael S. Branicky, Jan 08 2022

Crossrefs

Cf. A119834, A119835.

Sequence in context: A059498 A247147 A158085 * A127049 A142885 A108547

Adjacent sequences: A119830 A119831 A119832 * A119834 A119835 A119836

Keyword

nonn,more

Author

Pierre CAMI, May 25 2006

Extensions

a(13) from Michael S. Branicky, Jan 08 2022

a(14) from Michael S. Branicky, May 14 2023

Status

approved